JORDI GALÍ
J. DAVID LÓPEZ-SALIDO
JAVIER VALLÉS
Rule-of-Thumb Consumers and the Design
of Interest Rate Rules
We introduce rule-of-thumb consumers in an otherwise standard dynamic
sticky price model, and show how their presence can change dramatically
the properties of widely used interest rate rules. In particular, the existence
of a unique equilibrium is no longer guaranteed by an interest rate rule that
satisfies the so-called Taylor principle. Our findings call for caution when
using estimates of interest rate rules in order to assess the merits of monetary
policy in specific historical periods.
JEL codes: E32, E52
Keywords: Taylor principle, interest rate rules, sticky prices, rule-of-thumb
consumers.
The study of the properties of alternative monetary policy
rules, and the assessment of their relative merits, has been one of the central themes
of the recent literature on monetary policy. Many useful insights have emerged from
that research, with implications for the practical conduct of monetary policy, and
for our understanding of its role in different macroeconomic episodes.
Among some of the recurrent themes, much attention has been drawn to the
potential benefits and dangers associated with simple interest rate rules. Thus, while it
We have benefited from comments by Bill Dupor, Ken West (the editor), an anonymous referee, and
participants at the JMCB–Chicago Fed Tobin’s Conference and the NBER Summer Institute, as well as
seminars at the Federal Reserve Board, BIS, CREI-UPF, George Washington University and the Bank
of Spain. All remaining errors are our own. Galı́ acknowledges financial support from DURSI (Generalitat
de Catalunya), MCYT (Grant SEC2002-03816), and the Bank of Spain. The views expressed in this
paper do not necessarily represent those of the Bank of Spain.
Jordi Galı́ is Director and Senior Researcher with CREI and professor, Department of
Economics, Universitat Pompeu Fabra, Barcelona. E-mail: jordi.gali@upf.edu J. David
López-Salido is Senior Economist in the Research Department, Bank of Spain. E-mail:
davidl@bde.es Javier Vallés is Head of the Research Division at the Research Department,
Bank of Spain. E-mail: valles@bde.es
Received July 16, 2003; and accepted in revised form January 22, 2004.
Journal of Money, Credit, and Banking, Vol. 36, No. 4 (August 2004)
Copyright 2004 by The Ohio State University
740 : MONEY, CREDIT, AND BANKING
has been argued that simple interest rate rules can approximate well the performance
of complex optimal rules in a variety of environments,1 those rules have also been
shown to contain the seeds of unnecessary instability when improperly designed.2
A sufficiently strong feedback from endogenous target variables to the short-term
nominal interest rate is often argued to be one of the requirements for the existence
of a locally unique rational expectations equilibrium and, hence, for the avoidance of
indeterminacy and fluctuations driven by self-fulfilling expectations. For a large
number of models used in applications that determinacy condition can be stated in
a way that is both precise and general: the policy rule must imply an eventual
increase in the real interest rate in response to a sustained increase in the rate
of inflation. In other words, the monetary authority must adjust (possibly gradually)
the short-term nominal rate more than one-for-one with changes in inflation. That
condition, which following Woodford (2001) is often referred to as the Taylor
principle, has also been taken as a benchmark for the purposes of evaluating the
stabilizing role of central banks’ policies in specific historical periods. Thus,
some authors have hypothesized that the large and persistent fluctuations in inflation
and output in the late 1960s and 1970s in the U.S. may have been a consequence
of the Federal Reserve’s failure to meet the Taylor principle in that period; by
contrast, the era of low and steady inflation that has characterized most of Volcker
and Greenspan’s tenure seems to have been associated with interest rate policies
that satisfied the Taylor principle.3
In this paper we show how the presence of non-Ricardian consumers may alter
dramatically the properties of simple interest rate rules, and overturn some of the
conventional results found in the literature. In particular, we analyze a standard
New Keynesian model modified to allow for a fraction of consumers who do not
borrow or save in order to smooth consumption, but instead follow a simple ruleof-thumb: each period they consume their current labor income.
To anticipate our main result: when the central bank follows a rule that implies
an adjustment of the nominal interest rate in response to variations in current inflation
and output, the size of the inflation coefficient that is required in order to rule out
multiple equilibria is an increasing function of the weight of rule-of thumb consumers
in the economy (for any given output coefficient). In particular, we show that if the
weight of such rule-of-thumb consumers is large enough, a Taylor-type rule must
imply a (permanent) change in the nominal interest rate in response to a (permanent)
change in inflation that is significantly above unity, in order to guarantee the uniqueness of equilibrium. Hence, the Taylor principle becomes too weak a criterion for
stability when the share of rule-of-thumb consumers is large.
1. This is possibly the main conclusion from the contributions to the Taylor (1999a) volume.
2. See, e.g., Kerr and King (1996), Bernanke and Woodford (1997), Taylor (1999b), Clarida, Galı́,
and Gertler (2000), and Benhabib, Schmitt-Grohé, and Uribe (2001a,b), among others.
3. See, e.g., Taylor (1999b) and Clarida, Galı́, and Gertler (2000). Orphanides (2001) argues that the
Fed’s failure to satisfy the Taylor principle was not intentional; instead it was a consequence of a
persistent bias in their real-time measures of potential output.
JORDI GALÍ, J. DAVID LÓPEZ-SALIDO, AND JAVIER VALLÉS : 741
We also find that, independently of their weight in the economy, the presence of
rule-of-thumb consumers cannot in itself overturn the conventional result on the
sufficiency of the Taylor principle. Instead, we argue that it is the interaction of
those consumers with countercyclical markups (resulting from sticky prices in our
model) that lies behind our main result.
In addition to our analysis of a standard contemporaneous rule, we also investigate
the properties of a forward-looking interest rate rule. We show that the conditions
for a unique equilibrium under such a rule are somewhat different from those in a
contemporaneous one. In particular, we show that when the share of rule-of-thumb
consumers is sufficiently large it may not be possible to guarantee a (locally) unique
equilibrium or, if it is possible, it may require that interest rates respond less than
one-for-one to changes in expected inflation.
Our framework shares most of the features of recent dynamic optimizing sticky
price models.4 The only difference lies in the presence of rule-of-thumb consumers,
who are assumed to coexist with conventional Ricardian consumers. While the
behavior that we assume for rule-of-thumb consumers is admittedly simplistic (and
justified only on tractability grounds), we believe that their presence captures an
important aspect of actual economies which is missing in conventional models.
Empirical support of non-Ricardian behavior among a substantial fraction of households in the U.S. and other industrialized countries can be found in Campbell and
Mankiw (1989). It is also consistent, at least prima facie, with the findings of a
myriad of papers rejecting the permanent income hypothesis on the basis of aggregate
data. While many authors have stressed the consequences of the presence of rule-ofthumb consumers for fiscal policy,5 the study of its implications for the design
of monetary policy is largely non-existent.6
A number of papers in the literature have also pointed to some of the limitations
of the Taylor principle as a criterion for the stability properties of interest rate
rules, in the presence of some departures from standard assumptions. Thus, Edge and
Rudd (2002) and Roisland (2003) show how the Taylor criterion needs to be strengthened in the presence of taxes on nominal capital income. Fair (2004) argues that
the Taylor principle is not a requirement for stability if aggregate demand responds to
nominal interest rates (as opposed to real rates) and inflation has a negative effect
on consumption expenditures (through its effects on real wages and wealth), as it is
the case in estimated versions of his multicountry model. Christiano and Gust (1999)
find that the stability properties of simple interest rate rules are significantly altered
when the assumption of limited participation is introduced. Benhabib, SchmittGrohé, and Uribe (2001a) demonstrate that an interest rate rule satisfying the Taylor
principle will generally not prevent the existence of multiple equilibrium paths
converging to the liquidity trap steady state that arises in the presence of a zero
4. See, e.g., Rotemberg and Woodford (1999), Clarida, Galı́, and Gertler (1999), and Woodford (2001).
5. See, e.g., Mankiw (2000) and Galı́, López-Salido, and Vallés (2003c).
6. A recent paper by Amato and Laubach (2003) constitutes an exception. In that paper the authors
derive the appropriate loss function that a benevolent central banker should seek to minimize in the
presence of habit formation and rule-of-thumb consumers.
742 : MONEY, CREDIT, AND BANKING
lower bound on nominal rates. The present paper can be viewed as complementing
that work, by pointing to an additional independent source of deviations from the
Taylor principle as a criterion for stability of monetary policy rules.
The rest of the paper is organized as follows. Section 1 lays out the basic model
and derives the optimality conditions for consumers and firms, as well as their loglinear counterparts. Section 2 contains an analysis of the equilibrium dynamics and
its properties under our baseline interest rate rule, with a special emphasis on the
conditions that the latter must satisfy in order to guarantee uniqueness. Section 3
examines the robustness of those results and the required modifications when a
forward-looking interest rate rule is assumed. Section 4 concludes.
1. A NEW KEYNESIAN MODEL WITH RULE-OF-THUMB CONSUMERS
The economy consists of two types of households, a continuum of firms producing
differentiated intermediate goods, a perfectly competitive final goods firm, and a
central bank in charge of monetary policy. Next we describe the objectives and
constraints of the different agents. Except for the presence of rule-of-thumb consumers, our framework corresponds to a conventional New Keynesian model with
staggered price setting à la Calvo used in numerous recent applications. A feature
of our model that is worth emphasizing is the presence of capital accumulation.
That feature has often been ignored in the recent literature, on the grounds that its
introduction does not alter significantly most of the conclusions.7 In our framework,
however, the existence of a mechanism to smooth consumption over time makes
the distinction between Ricardian and non-Ricardian consumers meaningful, thus
justifying the need for introducing capital accumulation explicitly.8
1.1 Households
We assume a continuum of infinitely-lived households, indexed by i ∈ [0,1]. A
fraction 1 – λ of households have access to capital markets where they can trade a full
set of contingent securities, and buy and sell physical capital (which they accumulate
and rent out to firms). We use the term optimizing or Ricardian to refer to that
subset of households. The remaining fraction λ of households do not own any assets
nor have any liabilities; they just consume their current labor income. We refer to
them as rule-of-thumb (or non-Ricardian) consumers. Different interpretations for the
latter include myopia, lack of access to capital markets, fear of saving, ignorance of
intertemporal trading opportunities, etc. Campbell and Mankiw (1989) provide some
7. Among the papers that introduce capital accumulation explicitly in a New Keynesian framework
we can mention King and Watson (1996), Yun (1996), Dotsey (1999), Kim (2000), and Dupor (2002).
8. Notice that in the absence of capital accumulation, the only difference in behavior across household
types would be a consequence of the fact that Ricardian households obtain some dividend income
from the ownership of firms. Yet, the existence of a market for firms’ stocks would not provide a means
to smooth consumption, since, in equilibrium, all shares would have to be held by Ricardian consumers in
equal proportions.
JORDI GALÍ, J. DAVID LÓPEZ-SALIDO, AND JAVIER VALLÉS : 743
evidence, based on estimates of a modified Euler equation, of the quantitative importance of such rule-of-thumb consumers in the U.S. and other industrialized
economies.
Optimizing households. Let Cto, and Lto represent consumption and leisure for
optimizing households (henceforth we use a superscript “o” to refer to optimizing
households’ variables). Preferences are defined by the discount factor β ∈ (0,1)
and the period utility U(Cto,Lto). Optimizing households seek to maximize
E0兺∞t⫽0βtU(Cto,Lto), where Lto ⫹ Nto ⫽ 1, subject to the sequence of budget constraints,
Pt(Cto ⫹ Ito) ⫹ Rt⫺1Bt⫹1 ⫽ Wt Nto ⫹ RktKto ⫹ Bt ⫹ Dt ,
(1)
and the capital accumulation equation
o
Kt⫹1
⫽ (1 ⫺ δ) Kto ⫹ φ
()
Ito
Kto
Kto .
(2)
Hence, at the beginning of the period the consumer receives labor income
Wt N ot (where Wt denotes the nominal wage), and income from renting his capital
holdings Kot to firms at the (nominal) rental cost Rkt. Bt is the quantity of nominally
riskless one-period bonds carried over from period t – 1, and paying one unit of
the numéraire in period t. Rt denotes the gross nominal return on bonds purchased
in period t. Dt are dividends from ownership of firms. PtCto and PtIto denote, respectively, nominal expenditures on consumption and capital goods. Capital adjustment
costs are introduced through the term φ(ItoⲐKot )Kot which determines the change in
the capital stock (gross of depreciation) induced by investment spending Ito. We
assume φ′ ⬎ 0, and φ′′ ≤ 0, with φ′(δ) ⫽ 1, and φ(δ) ⫽ δ. In what follows
1
we specialize the period utility to take the form U(C,L) ≡ 1 ⫺ σ(C Lν)1⫺σ where σ ≥
0 and ν ⬎ 0.
The first-order conditions for the optimizing consumer’s problem can be written as:
Cto
1 Wt
,
ν Pt
(3)
1 ⫽ RtEt{Λt,t⫹1} ,
(4)
Lto
⫽
{ [
(
PtQt ⫽ Et Λt,t⫹1 Rkt⫹1 ⫹ Pt⫹1Qt⫹1 (1 ⫺ δ) ⫹ φt⫹1 ⫺
1
Qt ⫽
φ′
()
Ito
Kto
,
( ) )]}
o
It⫹1
o
Kt⫹1
φ′t⫹1
,
(5)
(6)
744 : MONEY, CREDIT, AND BANKING
o
o
o
o
where φt⫹1 ≡ φ(It⫹1
ⲐKt⫹1
) and φ′t ⫹1 ≡ φ′(It⫹1
ⲐKt⫹1
) respectively; Λt,t⫹k is the stochastic
discount factor for nominal payoffs given by:
( )( ) ( )
Λt,t⫹k ≡ βk
o
Ct⫹k
⫺σ
Cto
o
Lt⫹k
Lto
ν(1⫺σ)
Pt
,
Pt⫹k
(7)
and where Qt is the (real) shadow value of capital in place, i.e., Tobin’s Q. Notice
that, under our assumption on φ, the elasticity of the investment-capital ratio with
respect to Q is given by ⫺(1Ⲑ(φ″(δ)δ)) ≡ η .
Rule-of-thumb households. Rule-of-thumb households do not attempt (or are just
unable) to smooth their consumption path in the face of fluctuations in labor income.
Each period they solve the static problem, i.e., they maximize their period utility
U(Ctr,Lrt ) subject to the constraint that all their labor income is consumed, that is:
PtCtr ⫽ WtNtr ,
(8)
and where an “r” superscript is used to denote variables specific to rule-of-thumb
households.
The associated first-order condition is given by:
Crt
Lrt
⫽
1 Wt
,
ν Pt
(9)
which combined with Equation (8) yields
Nrt ⫽
1
≡ Nr ,
1⫹ν
(10)
hence implying a constant employment for rule-of-thumb households,9 as well as
a consumption level proportional to the real wage:10
Crt ⫽
1 Wt
,
1 ⫹ ν Pt
(11)
Aggregation. Aggregate consumption and leisure are a weighted average of the
corresponding variables for each consumer type. Formally:
Ct ≡ λCtr ⫹ (1 ⫺ λ)Cto ,
Nt ≡
λNtr
⫹ (1 ⫺
λ)Nto
(12)
.
(13)
Similarly, aggregate investment and capital stock are given It ≡
and Kt ≡
(1⫺λ)Kto. We can combine Equations (12) and (13) with the optimality Conditions
(9), (10), and (11) to obtain,
(1⫺λ)Ito,
9. Alternatively we could have assumed directly a constant labor supply for rule-of-thumb households.
10. Notice that under our assumptions, real wages are the only source of fluctuations in rule-of-thumb
households’ disposable income. More realistically, as shown in Galı́, Lopez-Salido, and Valles (2003c),
the introduction of labor market frictions can generate fluctuations in hours of rule-of-thumb consumers, thus
implying a second margin of variation in disposable income. In that context, it may be possible to
preserve our findings even in the presence of wage stickiness (nominal or real). This constitutes a natural
extension of this paper and is part of our ongoing research.
JORDI GALÍ, J. DAVID LÓPEZ-SALIDO, AND JAVIER VALLÉS : 745
Nt ⫽
λ
⫹ (1 ⫺ λ) Nto
1⫹ν
Ct ⫽
1 Wt
(1 ⫺ Nt)
ν Pt
( )
(14)
which will be used below.
1.2 Firms
We assume the existence of a continuum of monopolistically competitive firms
producing differentiated intermediate goods. The latter are used as inputs by a
(perfectly competitive) firm producing a single final good.
Final goods firm. The final good is produced by a representative, perfectly competitive firm with a constant returns technology: Yt ⫽ (兰10Xt(j)(ε⫺1)/εdj)ε/(ε⫺1), where Xt( j)
is the quantity of intermediate good j used as an input. Profit maximization, taking
as given the final goods price Pt and the prices for the intermediate goods Pt(j), for
all j ∈ [0,1], yields the set of demand schedules, Xt( j) ⫽ (Pt( j)ⲐPt)⫺ε Yt . Finally,
the zero profit condition yields, Pt ⫽ (兰10Pt(j)1⫺εdj)1/1⫺ε .
Intermediate goods firm. The production function for a typical intermediate goods
firm (say, the one producing good j) is given by:
Yt( j) ⫽ Kt( j)αNt( j)1⫺α
(15)
where Kt( j) and Nt( j) represents the capital and labor services hired by firm j.11
Cost minimization, taking the wage and the rental cost of capital as given, implies
the optimality condition
( )(
)
α
Wt
Kt(j)
.
⫽
Nt(j)
1 ⫺ α Rkt
Hence, real marginal cost is common to all firms and given by:
MCt ⫽
( )( )
1 Rkt
Φ Pt
α
Wt
Pt
1⫺α
,
where Φ ≡ αα(1 – α)1–α.
Price setting. Intermediate firms are assumed to set nominal prices in a staggered
fashion, according to the stochastic time dependent rule proposed by Calvo (1983).
Each firm resets its price with probability 1 – θ each period, independently of the
11. Without loss of generality we have normalized the level of total factor productivity to unity.
746 : MONEY, CREDIT, AND BANKING
time elapsed since the last adjustment. Thus, for each period a measure 1 – θ of
producers reset their prices, while a fraction θ keep their prices unchanged
A firm resetting its price in period t will seek to maximize
∞
max Et
∗
{Pt }
兺θ E {Λ
k
t
∗ ⫺ Pt⫹kMCt⫹k)} ,
t,t⫹kYt⫹k(j)(Pt
k⫽0
⫺ε
subject to the sequence of demand constraints, Yt⫹k( j) ⫽ Xt⫹k( j) ⫽ (P*t ⲐPt⫹k) Yt⫹k
where P*t represents the price chosen by firms resetting prices at time t. The firstorder condition for this problem is:
兺θ E {Λ
∞
k
t
t,t⫹kYt⫹k( j)
k⫽0
(
P*t ⫺
)}
ε
Pt⫹k MCt⫹k
ε⫺1
⫽0
(16)
Finally, the equation describing the dynamics for the aggregate price level is
1
* 1⫺ε 1⫺ε
] .
given by Pt ⫽ [θP1⫺ε
t⫺1 ⫹ (1 ⫺ θ)(Pt )
1.3 Monetary Policy
The central bank is assumed to set the nominal interest rate rt ≡ Rt – 1 every
period according to a simple linear interest rate rule:
rt ⫽ r ⫹ φππt ⫹ φyyt
(17)
where φπ ≥ 0, φy ≥ 0, and r is the steady-state nominal interest rate, and where πt,
Yt represent inflation and output deviations from steady state. Notice that the rule
above implicitly assumes a zero inflation target, which is consistent with the steady
state around which we will log-linearize the price-setting Equation (16). A rule
analogous to Rule (17) was originally proposed by John Taylor (Taylor 1993) as a
description for the evolution of short-term interest rates in the U.S. under Greenspan.
It has since become known as the Taylor rule and has been used in numerous
theoretical and empirical applications.12 In addition to Rule (17), we also analyze the
properties of a forward-looking interest rate rule, in which interest rates respond to
expected inflation and output. We refer the reader to the discussion below for details.
1.4 Market Clearing
The clearing of factor and good markets requires that the following conditions
1
1
are satisfied for all t: Nt ⫽ 兰 Nt( j)dj, Kt ⫽ 兰 Kt( j)dj, Yt( j) ⫽ Xt( j), for all j ∈ [0,1] and
0
Yt ⫽ Ct ⫹ It .
0
(18)
1.5 Linearized Equilibrium Conditions
Next we derive the log-linear versions of the key optimality and market clearing
conditions that will be used in our analysis of the model’s equilibrium dynamics.
12. This is illustrated in many of the papers contained in the Taylor (1999) volume, which analyze
the properties of rules like Rule (17) or variations thereof in the context of a variety of models.
JORDI GALÍ, J. DAVID LÓPEZ-SALIDO, AND JAVIER VALLÉS : 747
For aggregate variables we generally use lower case letters to denote the logs of
the corresponding original variables (or their log deviations from steady state), and
ignore constant terms throughout. Some of these conditions hold exactly, while
others represent first-order approximations around a zero inflation steady state.
Households. The log-linearized versions of the households’ optimality conditions,
expressed in terms of aggregate variables, are presented next. The reader can find
details of the derivations in a companion working paper.13 Some of these optimality
conditions turn out to be independent of λ, the weight of rule-of-thumb consumers
in the economy. Among the latter we have the aggregate labor supply schedule that
can be derived taking logs on both sides of Equation (3):
ct ⫹ ϕnt ⫽ wt ⫺ pt ,
(19)
where ϕ ≡ NⲐ1 ⫺ N. The latter coefficient, which can be interpreted as the inverse
of the Frisch aggregate labor supply elasticity, can be shown to be independent of λ.14
The log-linearized equations describing the dynamics of Tobin’s Q (Equation 6)
and its relationship with investment (Equation 5) are also independent of λ, and
given, respectively, by
qt ⫽ βEt{qt⫹1} ⫹ [1 ⫺ β(1 ⫺ δ)]Et{(rkt⫹1 ⫺ pt⫹1)} ⫺ (rt ⫺ Et{πt⫹1})
(20)
it ⫺ kt ⫽ ηqt
(21)
and
The same invariance to λ holds for the log-linearized capital accumulation
equation:
kt⫹1 ⫽ δit ⫹ (1 ⫺ δ)kt
(22)
The only aggregate equilibrium condition that is affected by the weight of ruleof-thumb consumers turns out to be the log-linearized aggregate Euler equation,
which takes the form
ct ⫽ Et{ct⫹1} ⫺
where
1
(rt ⫺ Et{πt⫹1} ⫺ ρ) ⫺ ΘEt{∆nt⫹1} ,
σ
( )
1
νϕ
σ
ϕλγr
Cr
ν
1
Θ≡
⫹
, and γr ≡ ⫽
僆 (0, 1) .
1 ⫺ λγr
1 ⫺ λγr
C 1⫹ν1⫺N
1⫺
13. See Galı́, López-Salido, and Vallés (2003a).
14. More specifically, ϕ is given by:
ϕ≡
1
(ρ ⫹ δ)(1 ⫺ α)
N
⫽
.
1 ⫺ N ν ρ ⫹ δ(1 ⫺ α) ⫹ µ(ρ ⫹ δ)
(23)
748 : MONEY, CREDIT, AND BANKING
Notice that the possibility of a non-separable utility (σ ≠ 1) justifies in itself the
presence of the term involving expected employment growth in the aggregate Euler
equation. Notice, however, that in the absence of rule-of-thumb consumers we have
Θ ⫽ (1 ⫺ (1Ⲑσ))νϕ ⬍ 1, since νϕ 僆 ( (0,1). In general, however, the size of Θ is a
highly non-linear function of λ, the weight of rule-of-thumb consumers. As discussed
below, that effect can potentially alter the local stability properties of the dynamical
system describing the equilibrium.
Firms. Log-linearization of Equation (16) and the definition of aggregate price
level, around the zero inflation steady state, yields the familiar equation describing
the dynamics of inflation as a function of the deviations of the average (log) markup
from its steady state level
πt ⫽ βEt{πt⫹1} ⫺ τµt
(24)
where
τ⫽
(1 ⫺ βθ)(1 ⫺ θ)
,
θ
and (ignoring constant terms)
µt ⫽ (yt ⫺ nt) ⫺ (wt ⫺ pt) ⫽ (yt ⫺ kt) ⫺ (rkt ⫺ pt) .
(25)
Furthermore, it can be shown that the following aggregate production function
holds, up to a first-order approximation:
yt ⫽ αkt ⫹ (1 ⫺ α)nt
(26)
Market clearing. Log-linearization of the market clearing condition of the final
good around the steady state yields:
yt ⫽ γcct ⫹ (1 ⫺ γc)it
where
γc ≡
C
⫽1⫺
Y
(27)
( )
δα 1 ⫺
1
ε
( ρ ⫹ δ)
,
is the aggregate consumption share in the steady state, which is independent of the
weight of rule-of-thumb consumers.
2. ANALYSIS OF EQUILIBRIUM DYNAMICS
We can now combine equilibrium Conditions (19)–(27) to obtain a system of
difference equations describing the log-linearized equilibrium dynamics of our model
JORDI GALÍ, J. DAVID LÓPEZ-SALIDO, AND JAVIER VALLÉS : 749
economy. After several straightforward though tedious substitutions, we can reduce
that system to one involving four variables:
AEt{xt⫹1} ⫽ Bxt ,
(28)
where xt ≡ (nt, ct, πt, kt)′. Notice that nt, ct, πt, kt are expressed in terms of log
deviations from their values in the zero inflation steady state. The elements of
matrices A and B are all functions of the underlying structural parameters.15
Notice that xt ⫽ 0 for all t, which corresponds to the perfect foresight zero
inflation steady state, always constitutes a solution to the above system. This should
not be surprising, given that for simplicity we have not introduced any fundamental
shocks in our model. In the remainder of the paper we study the conditions under
which the solution to Equation (28) is unique and converges to the steady state,
for any given initial capital stock. In doing so we restrict our analysis to solutions
of Equation (28) (i.e., equilibrium paths) which remain within a small neighborhood of
the steady state.16 Before we turn to that task, we discuss briefly the calibration that
we use as a baseline for that analysis.
2.1 Baseline Calibration
The model is calibrated to a quarterly frequency. Table 1 summarizes compactly
the values assumed for the different parameters in the baseline calibration. The rate
of depreciation δ is set to 0.025 (implying a 10% annual rate). The elasticity of output
with respect to capital, α, is assumed to be 1/3, a value roughly consistent with the
observed labor income share given any reasonable steady state markup. With regard
to preference parameters, we set the discount factor β equal to 0.99 (implying a
steady state real annual return of 4%). The elasticity of substitution across intermediate goods, ε, is set to 6, a value consistent with a steady state markup µ of 0.2. The
previous parameters are kept at their baseline values throughout the present section.
Next we turn to the parameters for which some sensitivity analysis is conducted,
by examining a range of values in addition to their baseline settings. We set
the baseline value for parameter ν in a way consistent with a unit Frisch elasticity
of labor supply (i.e., ϕ ⫽ 1) in our baseline calibration. That choice is associated
with a fraction of time allocated to work in the steady state given by N ⫽ 1/2. We
choose a baseline value of one for σ, which corresponds to a separable (log–log)
utility specification. The fraction of firms that keep their prices unchanged, θ, is
given a baseline value of 0.75, which corresponds to an average price duration of
1 year. This is consistent with the findings reported in Taylor (1999c). Following
King and Watson (1996), we set η, the elasticity of investment with respect to
Tobin’s Q, equal to 1.0 under our baseline calibration.17 Finally, we set φπ ⫽ 1.5
15. See the appendix in Galı́, López-Salido, and Vallés (2003a).
16. See, e.g., Benhabib, Schmitt-Grohé, and Uribe (2001a) for a discussion of the caveats associated
with that approach.
17. Other authors who have worked with an identical specification of capital adjustment costs have
considered alternative calibrations of that elasticity. Thus, e.g., Dotsey (1999) assumes an elasticity of
0.25; Dupor (2002) assumes a baseline elasticity of 5; Baxter and Crucini (1993) set a baseline value
of 15; Abel (1980) estimates that elasticity to be between 0.3 and 0.5.
750 : MONEY, CREDIT, AND BANKING
TABLE 1
Baseline Calibration
Parameters
Values
Description of the parameters
δ
α
β
ε
ϕ
σ
θ
η
φπ
φy
0.025
1/3
0.99
6
1
1
3/4
1
1.5
0.5
Depreciation rate
Elasticity of output with respect to capital
Discount factor
Elasticity of substitution among intermediate goods
Inverse of the (Frisch) labor supply elasticity
Relative risk aversion
Fraction of firms that leave their prices unchanged
Elasticity of investment to Tobin’s Q
Inflation coefficient in interest rate rule
Output coefficient in interest rate rule
and φy ⫽ 0.5 as the baseline values for the interest rate rule coefficients, in a way
consistent with Taylor’s (1993) characterization of U.S. monetary policy under
Greenspan.
Much of the sensitivity analysis below focuses on the weight of rule-of-thumb
households (λ) and its interaction with θ, σ, ϕ, η, and φπ and φy.
2.2 Determinacy Analysis
Vector xt contains three non-predetermined variables (hours, consumption, and
inflation) and a predetermined one (capital stock). Hence, the solution to Equation
(28) is unique if and only if three eigenvalues of matrix A–1B lie outside the unit
circle, and one lies inside.18 Alternatively, if there is more than one eigenvalue of
A–1B inside the unit circle the equilibrium is locally indeterminate: for any initial
capital stock there exists a continuum of deterministic equilibrium paths converging
to the steady state, and the possibility of stationary sunspot fluctuations arises.
On the other hand, if all the eigenvalues A–1B lie outside the unit circle, there is no
solution to Equation (28) that converges to the steady state, unless the initial
capital stock happens to be at its steady state level (in which case xt ⫽ 0 for all t is
the only non-explosive solution). Below our focus is on how the presence of ruleof-thumb consumers may influence the configuration of eigenvalues of the dynamical
system, and hence the properties of the equilibrium.
2.3 The Taylor Principle and Indeterminacy
We start by exploring the conditions for the existence of a unique equilibrium as
a function of the degree of price stickiness (indexed by parameter θ) and the weight
of rule-of-thumb households (indexed by parameter λ) under an interest rate rule
like Rule (17). As shown by Bullard and Mitra (2002) and Woodford (2001), in a
version of the model above with neither capital nor rule-of-thumb consumers,
18. See, e.g., Blanchard and Kahn (1980).
JORDI GALÍ, J. DAVID LÓPEZ-SALIDO, AND JAVIER VALLÉS : 751
a necessary and sufficient condition for the existence of a (locally) unique equilibrium
is given by19
φπ ⬎ 1 ⫺
(1 ⫺ β) φy
τ(1 ⫹ ϕ)
(29)
A rule like Rule (17) which meets the condition above is said to satisfy the Taylor
principle. As discussed in Woodford (2001), such a rule guarantees that in response
to permanent change in inflation (and, hence, in output), the nominal interest rate is
adjusted more than one-for-one. In the particular case of a zero coefficient on output
the Taylor principle is satisfied whenever φπ ⬎ 1. More generally, as Equation (29)
makes clear, it is possible for the equilibrium to be unique for values of φπ ⬍ 1,
as long as the central bank raises the interest rate sufficiently in response to an
increase in output. In other words, in the canonical model there is some substitutability between the size of the response to output and that of the response to inflation.
As shown in Dupor (2002) and further illustrated below, the previous finding carries
over, at least qualitatively, to a version of the model with capital accumulation and
fully Ricardian consumers. In particular, when φy ⫽ 0 the condition for uniqueness
is given by φπ ⬎ 1.
Next we analyze the extent to which those conditions need to be modified in
order to guarantee the existence of a unique equilibrium in the model with rule-ofthumb consumers laid out above. A key finding of our paper is illustrated by Figure
1. That figure represents the equilibrium properties of our model economy for all
configurations of λ and θ, under the assumption of φπ ⫽ 1.5 and φy ⫽ 0.5, parameter
values that clearly satisfy the Taylor criterion in standard models. In particular, the
figure displays the regions in the parameter space (λ, θ) that are associated with
the presence of uniqueness and multiplicity of a rational expectations equilibrium
in a neighborhood of the steady state. Notice that each graph corresponds to an
alternative pair of settings for the risk aversion coefficient σ and the inverse labor
supply elasticity ϕ.
A key finding emerges clearly: the combination of a high degree of price stickiness
with a large share of rule-of-thumb consumers rules out the existence of a unique
equilibrium converging to the steady state. Instead, the economy is characterized
in that case by indeterminacy of equilibrium (dark region). Conversely, if (a) prices are
sufficiently flexible (low θ) and/or (b) the share of rule-of-thumb consumers is
sufficiently small (low λ), the existence of a unique equilibrium is guaranteed. That
finding holds irrespective of the assumed values for σ and ϕ, even though the
relative size of the different regions can be seen to depend on those parameters. In
particular, the size of the uniqueness region appears to shrink as σ and ϕ increase.
In sum, as made clear by Figure 1, the Taylor principle may no longer be a useful
criterion for the design of interest rate rules in economies with strong nominal rigidities
and a substantial weight of rule-of-thumb consumers.
19. As in Bullard and Mitra (2002), we restrict ourselves to non-negative values of φπ and φy.
752 : MONEY, CREDIT, AND BANKING
Fig. 1. Rule-of-thumb consumers, price stickiness. and indeterminacy. Note: simulations are based on the parameter
values of Table 1 and the baseline Taylor rule with ΦΠ ⫽ 1.5 and Φy ⫽ 0.5
Importantly, while the previous result has been illustrated under the assumption
of φπ ⫽ 1.5 and φy ⫽ 0.5 (the values proposed by Taylor, 1993), similar patterns
arise for a large set of configurations of those coefficients that would be associated
with the existence of a unique equilibrium in the absence of rule-of-thumb consumers.
The size of the indeterminacy region can be shown to shrink gradually as the size
of the interest rate response to inflation and output increases (while keeping other
parameters constant). In particular, for any given value of the output coefficient, φy
(and given a configuration of settings for the remaining parameters), the minimum
threshold value for the inflation coefficient φπ consistent with an unique equilibrium lies above the one corresponding to the model without rule-of-thumb consumers.
In other words, a strengthened condition on the size of the response of interest rates
to changes in inflation is required in that case. Next, we provide an explicit analysis
JORDI GALÍ, J. DAVID LÓPEZ-SALIDO, AND JAVIER VALLÉS : 753
of the variation in the threshold value for φπ , as a function of different parameter
values and, most importantly, as a function of the share of rule-of-thumb households.
2.4 Interest Rate Rules and Rule-of-Thumb Consumers: Requirements
for Stability
Figure 2 plots the threshold value of φπ that is required for a unique equilibrium
as a function of the share of rule-of-thumb consumers, for three alternative values
of φy: 0.5 (our baseline case), 0.0 (the pure inflation targeting case) and 1.0 (as in
the modified Taylor rule considered in Taylor, 1999c). For convenience, we plot the
inverse of the threshold value of φπ.20 We notice that as φy increases, the threshold
value for φπ falls, for any given share of rule-of-thumb consumers. Yet, as Figure
2 makes clear, the fact that the central bank is responding to output does not relieve it
from the need to respond to inflation on a more than one-for-one basis, once a
certain share of rule-of-thumb consumers is attained. Furthermore, as in our baseline
case, the size of the minimum required response is increasing in that share. Thus,
for instance, when φy ⫽ 0.0 the central bank needs to vary the nominal rate in
response to changes in inflation on a more than one-for-one basis whenever the
share of rule-of-thumb consumers is above 0.57.21 In particular, when λ ⫽ 2/3,
Fig. 2. Rule-of-thumb consumers and the threshold inflation coefficient. Note: simulations are based on the parameter
values of Table 1 and the baseline Taylor rule. The threshold inflation coefficient is the lowest value of ΦΠ that
guarantees a unique solution
20. The inverse of the threshold value is bounded, which facilitates graphical display.
21. It is worth pointing out that, for very high values of the rule-of-thumb consumers and a zero or
near-zero response to input in the interest rate rule, an inflation coefficient positive but close to zero
can also generate determinate equilibrium. That result is qualitatively similar to the one we obtain below
when we analyze the forward looking rule.
754 : MONEY, CREDIT, AND BANKING
the inflation coefficient φπ must lie above 6 (approximately) in order to guarantee
a unique equilibrium. Even though our simple-minded rule-of-thumb consumers do
not have a literal counterpart that would allow us to determine λ with precision,
we view these values as falling within the range of empirical plausibility given some
of the existing micro and macro evidence. In particular, estimated Euler equations
for aggregate consumption whose specification allows for the presence of rule-ofthumb consumers point to values for λ in the neighborhood of 1/2 (Campbell and
Mankiw 1989). In addition, and as recently surveyed in Mankiw (2000), recent
empirical microeconomic evidence tends to support that finding. 22
Figures 3a–3d, display similar information for alternative calibrations of θ, ϕ, η,
and σ, respectively, with all other parameters set at their baseline values in each
case. For convenience we set φy ⫽ 0, for in that case the Taylor principle takes a very
simple form: the threshold value for φπ in the absence of rule-of-thumb consumers
is equal to 1, which provides a convenient benchmark. The picture that emerges is,
qualitatively, similar to that of Figure 2 with φy ⫽ 0. Notice first that, in every case
considered, the threshold value for φπ is equal to 1, so long as the weight of rule-ofthumb consumers is sufficiently low. Once a certain weight for λ is attained, the
lower bound for φπ can be seen to increase rapidly with the share of rule-of-thumb
consumers. Regarding the influence of the parameters under consideration, the main
qualitative findings can be summarized as follows: the deviation from the Taylor
principle criterion seems to become more likely and/or quantitatively larger the
stronger the degree of price stickiness (i.e., the higher θ is), the lower the labor supply
elasticity (i.e., the higher ϕ is), the more convex capital adjustment costs are (i.e.,
the lower η is), and the higher the risk aversion parameter σ.
2.5 Impulse Responses and Economic Mechanisms
As discussed above, in the standard New Keynesian framework with a representative consumer, the Taylor principle generally constitutes the appropriate criterion
for determining whether an interest rate rule of the sort considered in the literature
will guarantee or not a unique equilibrium, and thus rule out the possibility of
sunspot-driven fluctuations. The basic intuition goes as follows. Suppose that, in
the absence of any shock to fundamentals that could justify it, there was an increase
in the level of economic activity, with agents anticipating the latter to return only
gradually to its original (steady state) level. That increase in economic activity would
be associated with increases in hours, lower markups (because of sticky prices),
and persistently high inflation (resulting from the attempts by firms adjusting prices
to re-establish their desired markups). But an interest rate rule that satisfied the
Taylor principle would generate high real interest rates along the adjustment path,
and hence, would call for a low level of consumption and investment relative to
the steady state. The implied impact on aggregate demand would make it impossible
22. Empirical estimates of the marginal propensity to consume out of current income range from
0.35 up to 0.6 (see Souleles, 1999) or even 0.8 (see Shea, 1995), values that are well above those implied
by the permanent income hypothesis. On the other hand Wolff (1998) reports that the mean net worth
of the lowest two quintiles of the US wealth distribution is only $900.
JORDI GALÍ, J. DAVID LÓPEZ-SALIDO, AND JAVIER VALLÉS : 755
Fig. 3. Rule-of-thumb consumers and the threshold inflation coefficient. Note: simulations are based on the parameter
values of Table 1 and the baseline Taylor rule under ΦY ⫽ 0. The threshold inflation coefficient is the lowest value of
ΦΠ that guarantees a unique solution
to sustain the initial boom, thus rendering it inconsistent with a rational expectations equilibrium.
Consider instead the dynamic response of the economy to such an exogenous
revision in expectations when the weight of rule-of-thumb consumers is sufficiently
high to allow for multiple equilibria even though the interest rate rule satisfies the
Taylor principle. That response is illustrated graphically in Figure 4, which displays
the simulated responses to an expansionary sunspot shock for a calibrated version
of our model economy meeting the above criteria. In particular we set φπ ⫽ 1.5,
φy ⫽ 0.5, and λ ⫽ 0.85. The presence of rule-of-thumb consumers, combined with
countercyclical markups, makes it possible to break the logic used above to rule
out a sunspot-driven variation in economic activity. Two features are critical
here. First, the decline in markups resulting from sluggish price adjustment allows
756 : MONEY, CREDIT, AND BANKING
Fig. 4. Dynamic responses to a sunspot shock. Note: simulations are based on the parameter values of Table 1 and
the baseline Taylor rule under Φπ ⫽ 1.5, Φy ⫽ 0.5, λ ⫽ 0.85
real wages to go up (this effect is stronger in economies with a low labor supply
elasticity) in spite of the decline in labor productivity associated with higher employment. Secondly, and most importantly, the increase in real wages generates a
boom in consumption among rule-of-thumb consumers. If the weight of the latter
in the economy is sufficiently important, the rise in their consumption will more
than offset the decline in that of Ricardian consumers, as well as the drop in
JORDI GALÍ, J. DAVID LÓPEZ-SALIDO, AND JAVIER VALLÉS : 757
aggregate investment (both generated by the rise in interest rates). As a result,
aggregate demand will rise, thus making it possible to sustain the persistent boom
in output that was originally anticipated by agents. That possibility is facilitated by
the presence of highly convex adjustment costs (low η), which will mute the
investment response, together with a low elasticity of intertemporal substitution (high
σ), which will dampen the response of the consumption of Ricardian households.
3. A FORWARD-LOOKING RULE
In the present section we analyze the properties of our model when the central
bank follows a forward-looking interest rate rule of the form
rt ⫽ r ⫹ φπEt{πt⫹1} ⫹ φyEt{yt⫹1} .
(30)
The rule above corresponds to a particular case of the specification originally
proposed by Bernanke and Woodford (1997), and estimated by Clarida, Galı́, and
Gertler (1998, 2000).23 Dupor (2002) analyzes the equilibrium properties of a rule
identical to Rule (30) in the context of a New Keynesian model with capital accumulation similar to the one used in the present paper, though without rule-of-thumb
consumers. His analysis suggests that the Taylor principle remains a useful criterion
for these kind of economies, but with an important additional constraint: φπ should
not lie above some upper limit φuπ ⬎ 1 (which in turn depends on φy) in order for
the rational expectations equilibrium to be (locally) unique. In other words, in
addition to the usual lower bound associated to the Taylor principle, there is an upper
bound to the size of the response to expected inflation that must be satisfied; if that
upper bound is overshot the equilibrium becomes indeterminate. A similar result has
been shown analytically in the context of a similar model without capital. See, e.g.,
Bernanke and Woodford (1997), and Bullard and Mitra (2002).24
How does the presence of rule-of-thumb consumers affect the previous result?
Figure 5 represents graphically the interval of φπ values for which a unique equilibrium exists, as a function of the weight of rule-of-thumb consumers λ, and for
alternative values of φy.
First, when φy ⫽ 0 and for low values of λ (roughly below 0.6) the qualitative
result found in the literature carries over to our economy: the uniqueness requires
that φπ lies within some interval bounded below by 1. Interestingly, for this region, the
size of that interval shrinks gradually as λ increases. That result is consistent
with the findings of Dupor (2002) for the particular case of λ ⫽ 0 (no rule-ofthumb consumers).
23. In Galı́, López-Salido, and Vallés (2003a) we also provide an analysis of the properties of a
backward-looking rule. For the most part those properties are qualitatively similar to those of a forwardlooking rule.
24. More recently, Levin, Wieland, and Williams (2003) have shown that the existence of such an
upper threshold is inherent to a variety of forward-looking rules, with the uniqueness region generally
shrinking as the forecast horizon is raised.
758 : MONEY, CREDIT, AND BANKING
Fig. 5. Rule-of-thumb consumers and indeterminacy. Note: simulations are based on the parameter values of Table
1 and the forward-looking Taylor rule
Most interestingly (and surprisingly), when the weight of rule-of-thumb consumers
λ lies above a certain threshold, the properties of the forward-looking rule change
dramatically. In particular, a value for φπ below unity is needed in order to
guarantee the existence of a unique rational expectations equilibrium. In other words,
the central bank would be ill advised if it were to follow a forward-looking rule
satisfying the Taylor principle, since that policy would necessarily generate an
indeterminate equilibrium.25
A systematic response of the interest rate to changes in output (φy ⬎ 0), even if
small in size, has a significant impact on the stability properties of our model
25. See Galı́, López-Salido, and Vallés (2003a) for a discussion of the reasons why a large presence
of rule-of-thumb consumers make it possible for a rule that responds less than one-for-one to (expected)
inflation to be consistent with a unique equilibrium. This result also applies to rules where the Central
Bank set interest rates in response to either current or past inflation (see Galı́, López-Salido, and
Vallés 2003a).
JORDI GALÍ, J. DAVID LÓPEZ-SALIDO, AND JAVIER VALLÉS : 759
economy. Thus, for low values of λ, a positive setting for φy tends to raise the upper
threshold for φπ consistent with a unique equilibrium. As seen in the four consecutive
graphs of Figure 5, the effect of φy on the size of the uniqueness region appears to
be non-monotonic, increasing very quickly for low values of φy and shrinking back
gradually for higher values. On the other hand, for higher values of λ, the opposite
effect takes place: the interval of φπ values for which there is a unique equilibrium
becomes smaller as we increase the size of the output coefficient relative to the φy ⫽ 0
case. In fact, under our baseline calibration, when φy ⫽ 0.5 and for λ sufficiently high,
an indeterminate equilibrium arises regardless of the value of the inflation coefficient.
The high sensitivity of the model’s stability properties to the size of the output
coefficient in a forward-looking interest rate rule in a model with capital accumulation
(but no rule-of-thumb consumers) had already been noticed by Dupor (2002). The
above analysis raises an important qualification (and warning) on such earlier results:
in the presence of rule-of-thumb consumers an aggressive response to output does
not seem warranted, for it can only reduce the region of inflation coefficients
consistent with a unique equilibrium. On the other hand, a small response to output
has the opposite effect: it tends to enlarge the size of the uniqueness region.
In summary, when the central bank follows a forward-looking rule like Rule (30)
the presence of rule-of-thumb consumers either shrinks the interval of φπ values for
which the equilibrium is unique (in the case of low λ), or makes a passive policy
necessary to guarantee that uniqueness (for high values of λ).
4. CONCLUDING REMARKS
The Taylor principle, i.e., the notion that central banks should raise (lower)
nominal interest rates more than one-for-one in response to a rise (decline) in
inflation, is generally viewed as a prima facie criterion in the assessment of a
monetary policy. Thus, an interest rate rule that satisfies the Taylor principle is
viewed as a policy with stabilizing properties, whereas the failure to meet the Taylor
criterion is often pointed to as a possible explanation for periods characterized by
large fluctuations in inflation and widespread macroeconomic instability.
In this paper we have provided a simple but potentially important qualification
to that view. We have shown how the presence of rule-of-thumb (non-Ricardian)
consumers in an otherwise standard dynamic sticky price model, can alter the properties of simple interest rate rules dramatically. The intuition behind the important role
played by rule-of-thumb consumers is easy to grasp: the behavior of those households
is, by definition, insulated from the otherwise stabilizing force associated with
changes in real interest rates. We summarize our main results as follows.
1. Under a contemporaneous interest rate rule, the existence of a unique equilibrium is no longer guaranteed by the Taylor principle when the weight of ruleof-thumb consumers attains a certain threshold. Instead the central bank may
be required to pursue a more anti-inflationary policy than would otherwise
be needed.
760 : MONEY, CREDIT, AND BANKING
2. Under a forward-looking interest rate rule, the presence of rule-of-thumb
consumers also complicates substantially the central bank’s task, by shrinking
the range of responses to inflation consistent with a unique equilibrium (when the
share of rule-of-thumb consumers is relatively low), or by requiring that a
passive interest rate rule is followed (when the share of rule-of-thumb consumers is large).
We interpret the previous results as calling for caution on the part of central banks
when designing their monetary policy strategies: the latter should not ignore the
potential importance of rule-of-thumb consumers (or, more broadly speaking, procyclical components of aggregate demand that are insensitive to interest rates). From
that viewpoint, our findings suggest that if the share of rule-of-thumb consumers is
non-negligible the strength of the interest rate response to contemporaneous inflation
may have to be increased in order to avoid multiple equilibria. But if that share
takes a high value, the size of the response required to guarantee a unique equilibrium
may be too large to be credible, or even to be consistent with a non-negative nominal
rate. In that case, our findings suggest that the central bank should consider adopting
a passive rule that responds to expected inflation only (as an alternative to a rule
that responds to current inflation with a very high coefficient). It is clear, however, that
such an alternative would have practical difficulties, especially from the viewpoint of
communication with the public.
The above discussion notwithstanding, it is not the objective of this paper to
come up with specific policy recommendations: our model is clearly too simplistic
to be taken at face value, and any sharp conclusion coming out of it might not be
robust to alternative specifications. On the other hand, we believe our analysis is
useful in at least one regard: it points to some important limitations of the Taylor
principle as a simple criterion for the assessment of monetary policy when rule-ofthumb consumers (or the like) are present in the economy. In that respect, our
findings call for caution when interpreting estimates of interest rate rules similar to
the ones analyzed in the present paper in order to assess the merits of monetary
policy in specific historical periods.26 In particular, our results suggest that evidence
on the size of the response of interest rates to changes in inflation should not
automatically be viewed as allowing for indeterminacy and sunspot fluctuations (if
the estimates suggest that the Taylor principle is not met) nor, alternatively, as
guaranteeing a unique equilibrium (if the Taylor principle is shown to be satisfied
in the data). Knowledge of the exact specification of the interest rate rule (e.g.,
whether it is forward looking or not) as well as other aspects of the model would
be required for a proper assessment of the stabilizing properties of historical monetary
policy rules. In addition to its implications for the stability of interest rate rules,
the presence of rule-of-thumb consumers is also likely to have an influence on the
nature of the central bank objective function. Early results along these lines, though
in the context of a model somewhat different from the one in this paper, can be
26. See, e.g., Taylor (1999b) and Clarida, Galı́, and Gertler (2000).
JORDI GALÍ, J. DAVID LÓPEZ-SALIDO, AND JAVIER VALLÉS : 761
found in Amato and Laubach (2003). We think that the derivation of optimal
monetary policy rules as well as the assessment of simple policy rules using a
welfare-based criteria can be a fruitful line of research.
More generally, we believe that the introduction of rule-of-thumb consumers in
dynamic general equilibrium models used for policy analysis not only enhances
significantly the realism of those models, but it can also allow us to uncover
interesting insights that may be relevant for the design of policies and helpful in
our efforts to understand many macroeconomic phenomena. An illustration of that
potential usefulness can be found in a companion paper (Galı́, López-Salido and
Valles 2003c), where we have argued that the presence of rule-of-thumb consumers
may help account for the observed effects of fiscal policy shocks, some of which are
otherwise hard to explain with conventional New Keynesian or neoclassical models.
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